2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121529By gluing together copies of an all-right angled Coxeter polytope a number of open hyperbolic 6-manifolds with Euler characteristic -1 are constructed. They are the first known examples of hyperbolic 6-manifolds having the smallest possible volume.More details added in the last section. To appear in Electronic Research Announcements of the AMSGeometric Topology57M50text